This invention relates in general to a method of treatment of quartz crystal resonators for varying the frequency vs. temperature (f vs. T) characteristics thereof in a desired manner. More particularly, the invention relates to a method of treating SC-cut quartz resonator blanks, or other doubly rotated cuts, in such a way that a desired f vs. T characteristic can be achieved. Unmodified resonator blanks of these types will inherently have a certain variation in f vs. T characteristic due to the inherent errors in the cutting machinery and due to variations introduced during lapping. The novel method of the invention permits all of these randomly varying blanks to be converted to the same characteristic, within an acceptable tolerance, or each to different desired characteristics.
The invention is based on the discovery that the f vs. T characteristic of the c-mode of SC-cut quartz resonators and of other doubly rotated cuts is a function of the curvature or diopter value of the convex side thereof and of the electrode area. By changing this diopter value and/or the electrode area, the slope of the f vs. T characteristic at its point of inflection, as well as the turning points thereof can be controlled in a predictable manner. These changes in diopter value and/or electrode area thus effectively change the effective angles of cut of the crystals and thus provides a relatively easy and inexpensive way of increasing the useability of crystal blanks which might otherwise have to be discarded or modified by other more costly methods. The diopter value, D, is a measure of the curvature of the convex side of these resonator blanks and is equal to the reciprocal of the radius of curvature in meters. The units of all of the slopes referred to herein is ppm/.degree.C.